〈A〉 tissue or voxel mean cell surface area

AQP aquaporin

AQP4 aquaporin 4

AQP4KO aquaporin 4 knock-out

ATP adenosine triphosphate

ATPi intracellular ATP

AWC active trans-membrane water cycling

ae ρ〈A〉

aH2O water thermodynamic activity

CEST chemical exchange saturation transfer

Δ G Gibbs free energy change

ΔG0 Standard AG

ΔGyyy ΔG for substrate, enzyme, reaction; YYY

ΔGYYY(effl) ΔG for YYY efflux

ΔGiYY(infl) ΔG for YYY influx

ΔHYYY(infl) enthalpy change for YYY influx

ΔTToi trans-cytolemmal osmotic gradient (in - out)

ΔSYYY(infl) entropy change for YYY influx

ΔV†† activation volume

d density (mass/volume)

EAAT1 excitatory amino acid transporter 1

Em,oi trans-membrane electrical potential (in - out)

effl an efflux process

FDG 2-deoxy-2-18Fluoro-D-glucose

fH2O water activity coefficient on the mole fraction scale (X)

fW tissue water volume fraction

fW,i intracellular fW

fW,o extracellular fW

ϕ osmotic coefficient

G Gibbs free energy

GABA γ-amino butyric acid

GAT 1 GABA transporter 1

GLUT1 glucose transporter 1

glc glucose

gln glutamine

glu glutamate−

γH2O water activity coefficient on the molality scale (m)

1H2O water proton MR signal

H2Oi intracellular water molecule

H2Oo extracellular water molecule

H3Oi+ intracellular hydronium ion

H3Oo+ extracellular hydronium ion

iGlutR an ionotropic glutamate’receptor

infl an influx process

Ki+ intracellular K+

Ko+ extracellular K+

KCC4 potassium, chloride transporter 4

k kinetic rate constant

kio cellular water efflux k (1/τi)

kio(a) active kio contribution

kio(p) passive kio contribution

koi(p) passive cellular water influx k contribution

M molarity concentration scale

MADI metabolic activity diffusion imaging

MCT1 mono-carboxylate transporter

MD molecular dynamics

MRI magnetic resonance imaging

MRyyy YYY metabolic rate

MRglu(consump) MR of glucose consumption

MRglu(infl) MR of glucose influx

MRGlu-gln(cycle) MR of glutamate’-glutamine cycling

MRO2 MR of O2 consumption

cMRYYY cellular metabolic rate for YYY process = tMRYYY/ρ

tMRYYY tissue metabolic rate for YYY process = /ρcMRYYY

MWH2O molecular mass (“weight”) of water

m molality concentration scale

mOsM milli-osmolarity concentration scale

mOsm milli-osmolality concentration scale

mOsX milli-osmole fraction concentration scale

μYYY chemical potential of YYY; (∂G/∂nYYY)T,p,n(≠ nYYY)

Nai+ intracellular Na+

Nao+ extracellular Na+

NKA Na+,K+-ATPase (sodium pump)

NKCC1 sodium, potassium, chloride transporter 1

NMR nuclear magnetic resonance

n number of moles

OsM osmolarity concentration scale

OsMYYY YYY OsM

Osm osmolality concentration scale

OsmYYY YYY Osm

OsX osmole fraction concentration scale

OsXYYYi intracellular YYY OsX

OsXYYY,o extracellular YYY OsX

P hydraulic (mechanical) pressure

P0 standard state P

Pd diffusional permeability coefficient (exchange)

Pd(p) passive Pd

PdYYY YYY Pd

Pf flux (flow) permeability coefficient

PfYYY YYY Pf

Pi intracellular P

Po extracellular P

PC potassium channel

PET positron emission tomography

p tissue water mole fraction (“population”)

pi intracellular p

po extracellular p

per permeant particle

R ideal gas constant

ρ cell (number) density

SYYY stoichiometric coefficient of YYY

SGLT sodium/glucose co-transporter

SS trans-cytolemmal NMR shutter-speed

TGN020 specific AQP4 inhibitor

τi mean H2Oi molecule lifetime (1/kio)

〈V〉 tissue or voxel mean cell volume

Vm volume molality concentration scale

Vmi intracellular Vm

Vmo extracellular Vm

v tissue volume fraction

ve extracellular v (ECV) (= 1 - vi)

vi intracellular v [pV]

X mole fraction concentration scale

XYYY YYY X

XYYY,i intracellular YYY X

XYYY,o extracellular YYY X

x water cycling stoichiometry [H2O/ATP]

x′ x for individual water co-transporter

[YYY] YYY concentration

[YYYc] compartmental YYY concentration

[YYYi] intracellular YYY concentration

[YYYo] extracellular YYY concentration

[YYYt] tissue YYY concentration = vi[YYYi] = ve[YYYo]

yL yocto liter (= 10−24 L = 1 (nm)3))

yH2O water activity coefficient on the molarity scale (M)

ZYYY signed electrical charge of YYY